{"paper":{"title":"Arithmetic expanders and deviation bounds for random tensors","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Jop Bri\\\"et, Shravas Rao","submitted_at":"2016-10-11T17:09:40Z","abstract_excerpt":"We prove hypergraph variants of the celebrated Alon-Roichman theorem on spectral expansion of sparse random Cayley graphs. One of these variants implies that for every prime $p\\geq 3$ and any $\\varepsilon > 0$, there exists a set of directions $D\\subseteq \\mathbb{F}_p^n$ of size $O_{p,\\varepsilon}(p^{(1-1/p +o(1))n})$ such that for every set $A\\subseteq \\mathbb{F}_p^n$ of density $\\alpha$, the fraction of lines in $A$ with direction in $D$ is within $\\varepsilon\\alpha$ of the fraction of all lines in $A$. Our proof uses new deviation bounds for sums of independent random multi-linear forms tak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03428","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}